
Welcome to my Set Theory Page
Set Theory: Foundations of Mathematics
The two axioms which define Intuitive Set Theory
are discussed below.

Ackermann Functions and Transfinite Ordinals
An important part of Cantor's set theory, which forms the
foundations of mathematics, is the concept of
transfinite ordinals. A systematic way of writing the sequence of
ordinals is given.
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Justification of the Continuum Hypothesis
Intuitive arguments are given to suggest that Continuum
Hypothesis should be accepted.
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Axiomatic Derivation of the Continuum Hypothesis
Continuum Hypothesis is derived from an axiom called Axiom of
Monotonicity.
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Real Set Theory
A set theory is defined in which Generalized Continuum Hypothesis
and Axiom of Choice are theorems.
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Intuitive Set Theory
A set theory is defined in which Skolem Paradox does not arise.
Also, there are no sets which are not Lebesgue measurable.
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Two Axioms to Extend ZermeloFraenkel Theory
Axiom of Monotonicity is used along with ZermeloFraenkel
set theory to derive Generalized Continuum Hypothesis.
Axiom of Fusion is used to investigate the cardinality
of the set of points in a unit interval.
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Visualization of Intuitive Set Theory
Intuitive Set Theory is defined as the theory we get when axioms of
Monotonicity and Fusion are added to ZF theory. Cardinals in the theory
are visualized using illustrations.
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White Hole, Black Whole, and The Book
Physical and intellectual spaces are visualized making use of concepts
from Intuitive Set Theory. A book containing all the proofs of mathematics
is called The Book.
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The Essence of Intuitive Set Theory
The ideas which motivated the defintion of intuitive set theory
are explained. Only a passing acquaintance with the transfinite
cardinals of Cantor is assumed on the part of the reader.
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Generalized Continuum Hypothesis and the Method of Fusing
The method of fusing explains the basis for the formulation of the
axioms of monotonicity and fusion, the two axioms which define intuitive
set theory.
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Generalized Continuum Hypothesis and the Axiom of Combinatorial Sets
Axiom of Combinatorial Sets is defined and used to derive generalized continuum
hypothesis.
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Definition of Intuitive Set Theory
Two axioms which define intuitive set theory, Axiom of Combinatorial
Sets and Axiom of Infinitesimals, are stated. Generalized continuum
hypothesis is derived from the first axiom, and the infinitesimal is
visualized using the latter axiom.
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Two Open Problems and a Conjecture in Mathematical Logic
The open problems attempt to extend ZermeloFraenkel set theory and
the conjecture suggests an extension of Godel's incompleteness theorems.
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Teaching Generalized Continuum Hypothesis
Generalized Continuum Hypothesis is derived from a
simple axiom called Axiom of Combinatorial Sets.
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The Mathematical Universe in a Nutshell
The mathematical universe discussed here gives models of
possible structures our physical universe can have.
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Derivation of Continuum Hypothesis from Axiom of Combinatorial Sets
Continuum Hypothesis is derived from an axiom called Axiom of Combinatorial Sets.
The derivation is simple enough to be understood by any novice, who has a passing
acquintance with cardinals of Cantor.
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The advantage with the intuitive set theory is that it allows
us to have a simple visualization of our physical and intellectual spaces.
K. K. Nambiar
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